I've got an old bike with a quill stem, and the headset arrangement has a nut, and a textured lock ring. I presume I should tighten with a combination of a spanner and mole grip. Is a mole grip the right tool for the job?
Daniel is right. If you tighten the knurled ring by hand, but not quite as hard as it will go, then use a large spanner to tighten the locknut down against it, which will tighten the race slightly more, you won't need any sort of pliers (or, less likely to damage anything, a strap wrench). You might need to back off and try again a few times to get the load right so it turns freely but without play.
I'll add that anything hand tight will come loose fairly soon. As the knurled race loosens it will start to damage itself an/or the ball bearings and cause sloppy handling and steering. I'm not saying that you want to torque the race down to the fork, but up against the lock nut as @alex suggests:
My point is that "by hand as hard as you can" won't be good enough. You will need a tool that can grip the knurled race evenly. A pair of slip-joint adjustable pliers which are the right size will work. You want to be able to get both sides of the pliers parallel with each other when gripping the race. Anything less will potentially slip and cause damage to the knurled surface. You might even be able to get a pair with plastic covers over the teeth to protect whatever you are gripping.
About mole grips or locking pliers for us in the US (http://en.wikipedia.org/wiki/Locking_pliers) I've never found a pair that were large enough to do this. Also, you lose the hand feedback that regular pliers give you. You won't know when the race is about to slip until its too late.
I believe this style is meant to be tightened by hand.
To tighten, start by tightening the knurled/textured upper race a little harder than you intend it to be once you're done.
Next, add the washer and screw on the locknut as hard as you can without tightening the race any more than it already is. Too tight and you may damage the races and need a new headset.
Then whilst holding the locknut still with a spanner, unscrew the race by hand as hard as you can. The idea is to be it clamped against the locknut so neither can move.
You may need to experiment with how tight you start to get the right tightness at the end.
PS. Mole grips are almost always the wrong tool.